Definable principal congruences and solvability (Q1001911)
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scientific article; zbMATH DE number 5509597
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Definable principal congruences and solvability |
scientific article; zbMATH DE number 5509597 |
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Definable principal congruences and solvability (English)
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19 February 2009
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A variety \(V\) is said to have Definable Principal Congruences (DPC) if there is a first-order formula that defines the principal congruences in all algebras of \(V\). In this paper, it is proved that in a locally finite variety with DPC, the solvable congruences are nilpotent, and the strongly solvable congruences are strongly abelian. Particularly, in a congruence-modular variety with DPC, every solvable algebra can be decomposed as a direct product of nilpotent algebras of prime power.
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definable principal congruences
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twin group
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right (strongly) nilpotent congruence
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abelian variety
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locally finite variety
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solvable congruences
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solvable algebras
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tame congruence theory
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